My, lots of things! It's a huge subject. I'll list a few big items, but you might take a look at some resources on the internet for more information. A nice starting point is the Wikipedia article on IPv6: http://en.wikipedia.org/wiki/Ipv6

A few advantages of IPv6 over IPv4:

Much larger address space: the 32-bit IPv4 space has no more big address blocks left, but the 128-bit IPv6 space has lots of room

No need for NAT: under IPv4, your ISP gives you only one IP address; with IPv6, you'd get 64 bits worth of addresses

No packet fragmentation: IPv6 endpoints are required to use MTU discovery. This avoids the performance-killing fragmentation that IPv4 routers have to do when packets are too large for at least one of the hops. This is my favorite IPv6 feature!

Of course, there are disadvantages:

Longer IP addresses: they are harder to write down or memorize, and they make editing DNS zone files more of a pain

IP-address syntax: the syntax for IPv6 addresses uses colons for separating 16-bit units. This makes it a bit harder to write and parse literal IP addresses in contexts where the colon normally specifies a port number (as in URL's)

No NAT: exposing all the endpoints on your LAN makes it more vital that you pay attention to the firewall rules at your router

Deployment is slow. Most ISP's still don't offer native IPv6, so if you want to try it, you likely have to use some kind of tunnelling technique. (I use Hurricane Electric and find that they do a good job.)

There's lots more to say. If you have more-specific questions, come back and ask them.